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This is the aptitude questions and answers section on "Alligation or Mixture" with detailed explanation for various interview, competitive examination and entrance test. Problems of three difficulty levels are given with detailed solution Description, explanation, so that it becomes easy to grasp the fundamentals.

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**Alligation:**

It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

*A process or rule for the solution of problems concerning the compounding or mixing of ingredients differing in price or quality.*

* Merrian – Webster Medical Dictionary*

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**Basic Formula:**

If two ingredients A and B of price x and y respectively are mixed and the price of resultant mixture is M (mean price)then the ratio (R) in which ingredients are mixed is given by, **the rule of allegation**

$$ R = ({M-y}/{x-M})$$

The above formula can be represented in diagram below, which in turn is more intuitive to grasp

Ingredient A Ingredient B

(Price x) (Price y)

\ /

Mean

(Price M)

/ \

(M – y) : (x – M)

Thus the required ratio is,

$$ R = ({M-y}/{x-M}) = ({y - M}/{M - x})$$

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**Replacement of Part of Solution Formula:**

Suppose a container contains a solution from which some quantity of solution is taken out and replaced with one of the ingredients. This process is repeated n times then,

$\text "Final Amount of ingredient that is not replaced" =$

$$\text"Initial Amount " * (\text" Vol. after removal"/\text"Vol. after replacing")^n$$

Above formula is not only true for absolute amounts but for ratios as well. So following formula is also valid:

$\text"Final ratio of ingredient not replaced to total " =$

$$\text"Initial ratio " * (\text" Vol. after removal"/\text"Vol. after replacing")^n$$

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